Notice that the head is moving, before, during and after impact. Also notice that his body rotates around the left side (instead of the center). (now the figure skater is looping around his left foot, instead of rotating around the spine)

The difference in these videos explain why Federer's FH is bigger, but with seemingly less effort.

Also, with a quiet head and eyes stay focused on the contact point, his FH is cleaner with better control, less vulnerable to break-downs.

By rotating one's body around the spine, one generates more speed towards the ball

I think the differing grips more than anything speerate their forehands. In order to hit Roddick's forehand big, he has a completely different body set up on the approach than Fed.

The full western grip that Andy uses facilitates more of a lower body powered motin than the standard Eastern grip of Fed. The power seems more vertically released through the stroke versus the more circular, horizontal path you describ ein Fed's.

You can't compare their FHs only around those 2 videos. We do not know what was going on immediately before hitting those FHs. Maybe, the footwork was wrong, etc. If you were asked to supply a video that showed how you hit your own FH, you'd look for THE ONE, not a randomly chosen one.

It's not the forehand that separates Federer from Roddick. If each was only allowed to hit forehands, then a match between those two would be pretty close. The difference between the two is that Federer plays better defense placing his slices much deeper and Federer also places his serves much better while Roddick goes for the bombs that Federer just blocks back with good depth. The forehands look very different technique-wise but they are both two of the best forehands in the game.

main difference is that Fed hits flat, A-Rod hits topspin. A_rod keeps ball in play with not many winners, Fed has more errors but an abundance of winners. If Roddick could learn to flatten out his forehand like he has his backhand he will be a much better player like he was in 03. HE reached number one with a serve and a flat forehand, he needs nothing else.

Actually I also noticed this when Roddick was playing against Yuzhny. So Roddick's bad habit is not only shot on this video.

Roddick's head moves before the ball contracts the racket, while if you look at Fed's video or pictures, his eyes are always, always on the ball during the contact, and they stay there for another 1 sec or 2, on both the FH and BH. This way, Fed will have better balance when he hits, and thus he has less errors. If you move your body parts such as your head when hitting, your body is not perfectly balanced to hit the ball. This also applies to serve. If you drop your head earlier, you will hit the ball into the net.

And Fed does not only use eastern forehand. He changes grips based on his position and his shots. He does use semi-western at the baseline.

Federer's forehand looks smooth while as Roddick's is violent. They're completely different motions. While Roddick moves his head a lot, he puts his whole body behind the shot, so credit to him.
Federer drives through the ball a little more while as Roddick windshield-wipes the heck outta the ball.